Fluctuations

Can we distiguish dead (passive) or alive (active) objects by examing their fluctuations?

Velocity Fluctuations: The stochastic equations look the same:

  • Langevin equation for a passive bead: 

  • Actively moving bead below the transtion to moving state: 

  • However, since there is no equilibrium constraint, the velocity distribution will not be Maxwell-Boltzmann

Trapped bead: Consider a bead in an optical (laser) trap


(Movie from the Theriot Lab)

  • The simplest theoretical model is a particle in a one-dimensional potential φ(x): 

  • For a passive bead, the position and velocity are independent in equilibrium

:

  • For an active bead, the position and velocity are correlated, and     <xv>≠0

What is the joint probability in this case?  (A numerical solution)